A publisher for a promising new novel figures fixed costs (overhead, advances, promotion, copy editing, typesetting, and so on) at $57,00, and variable costs (printing, paper, binding, shipping) at $2.90 for each book produced. If the book is sold to distributors for $11 each, how many must be produced and sold for the publisher to break even?

Question

A publisher for a promising new novel figures fixed costs​ (overhead, advances,​ promotion, copy​ editing, typesetting, and so​ on) at ​$​57,00, and variable costs​ (printing, paper,​ binding, shipping) at ​$2.90 for each book produced. If the book is sold to distributors for ​$11 ​each, how many must be produced and sold for the publisher to break​ even?

GPT 3.5 · Answer

Let X be the number of books produced and sold for the publisher to break even.
The total cost (TC) for producing and selling X books is given by: TC = Fixed costs + Variable costs
The fixed costs are $57,000.
The variable costs are $2.90 per book, so the total variable cost for X books is 2.90X.
The total revenue (TR) from selling X books is given by: TR = Selling price per book * Number of books = $11X
To break even, the total cost should be equal to the total revenue: TC = TR
So, 57,000 + 2.90X = 11X
Combining like terms: 11X - 2.90X = 57,000
8.1X = 57,000
Dividing both sides by 8.1: X = 57,000 / 8.1
X ≈ 7,049
Therefore, approximately 7,049 books must be produced and sold for the publisher to break even.